Basic properties
Modulus: | \(3204\) | |
Conductor: | \(1068\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(88\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1068}(407,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3204.cd
\(\chi_{3204}(35,\cdot)\) \(\chi_{3204}(143,\cdot)\) \(\chi_{3204}(323,\cdot)\) \(\chi_{3204}(359,\cdot)\) \(\chi_{3204}(431,\cdot)\) \(\chi_{3204}(503,\cdot)\) \(\chi_{3204}(575,\cdot)\) \(\chi_{3204}(647,\cdot)\) \(\chi_{3204}(683,\cdot)\) \(\chi_{3204}(719,\cdot)\) \(\chi_{3204}(755,\cdot)\) \(\chi_{3204}(827,\cdot)\) \(\chi_{3204}(863,\cdot)\) \(\chi_{3204}(1007,\cdot)\) \(\chi_{3204}(1151,\cdot)\) \(\chi_{3204}(1187,\cdot)\) \(\chi_{3204}(1223,\cdot)\) \(\chi_{3204}(1259,\cdot)\) \(\chi_{3204}(1439,\cdot)\) \(\chi_{3204}(1475,\cdot)\) \(\chi_{3204}(1583,\cdot)\) \(\chi_{3204}(1799,\cdot)\) \(\chi_{3204}(1907,\cdot)\) \(\chi_{3204}(1943,\cdot)\) \(\chi_{3204}(2123,\cdot)\) \(\chi_{3204}(2159,\cdot)\) \(\chi_{3204}(2195,\cdot)\) \(\chi_{3204}(2231,\cdot)\) \(\chi_{3204}(2375,\cdot)\) \(\chi_{3204}(2519,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{88})$ |
Fixed field: | Number field defined by a degree 88 polynomial |
Values on generators
\((1603,713,181)\) → \((-1,-1,e\left(\frac{7}{88}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 3204 }(1475, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{85}{88}\right)\) |